Algebra Examples

$2 x + 4 y = 28$ $- 2 y = x + 28$

Step 1

Graph $2 x + 4 y = 28$ .

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Subtract $2 x$ from both sides of the equation.

$4 y = 28 - 2 x$

Step 1.1.2

Divide each term in $4 y = 28 - 2 x$ by $4$ and simplify.

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Step 1.1.2.1

Divide each term in $4 y = 28 - 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{28}{4} + \frac{- 2 x}{4}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $4$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{28}{4} + \frac{- 2 x}{4}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{28}{4} + \frac{- 2 x}{4}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $28$ by $4$ .

$y = 7 + \frac{- 2 x}{4}$

Step 1.1.2.3.1.2

Cancel the common factor of $- 2$ and $4$ .

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Step 1.1.2.3.1.2.1

Factor $2$ out of $- 2 x$ .

$y = 7 + \frac{2 (- x)}{4}$

Step 1.1.2.3.1.2.2

Cancel the common factors.

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Step 1.1.2.3.1.2.2.1

Factor $2$ out of $4$ .

$y = 7 + \frac{2 (- x)}{2 (2)}$

Step 1.1.2.3.1.2.2.2

Cancel the common factor.

$y = 7 + \frac{2 (- x)}{2 \cdot 2}$

Step 1.1.2.3.1.2.2.3

Rewrite the expression.

$y = 7 + \frac{- x}{2}$

Step 1.1.2.3.1.3

Move the negative in front of the fraction.

$y = 7 - \frac{x}{2}$

Step 1.2

Rewrite in slope-intercept form.

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Step 1.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2.2

Reorder $7$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} + 7$

Step 1.2.3

Write in $y = m x + b$ form.

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Step 1.2.3.1

Reorder terms.

$y = - (\frac{1}{2} x) + 7$

Step 1.2.3.2

Remove parentheses.

$y = - \frac{1}{2} x + 7$

Step 1.3

Use the slope-intercept form to find the slope and y-intercept.

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Step 1.3.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{1}{2}$

$b = 7$

Step 1.3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{1}{2}$

y-intercept: $(0, 7)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 7)$

Step 1.4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 1.4.1

Write in $y = m x + b$ form.

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Step 1.4.1.1

Reorder $7$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} + 7$

Step 1.4.1.2

Reorder terms.

$y = - (\frac{1}{2} x) + 7$

Step 1.4.1.3

Remove parentheses.

$y = - \frac{1}{2} x + 7$

Step 1.4.2

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 7 \\ 2 & 6 \end{array}$

Step 1.5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- \frac{1}{2}$

y-intercept: $(0, 7)$

$\begin{array}{c} x & y \\ 0 & 7 \\ 2 & 6 \end{array}$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 7)$

$\begin{array}{c} x & y \\ 0 & 7 \\ 2 & 6 \end{array}$

Step 2

Graph $- 2 y = x + 28$ .

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Step 2.1

Divide each term in $- 2 y = x + 28$ by $- 2$ and simplify.

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Step 2.1.1

Divide each term in $- 2 y = x + 28$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{x}{- 2} + \frac{28}{- 2}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $- 2$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{x}{- 2} + \frac{28}{- 2}$

Step 2.1.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{- 2} + \frac{28}{- 2}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{28}{- 2}$

Step 2.1.3.1.2

Divide $28$ by $- 2$ .

$y = - \frac{x}{2} - 14$

Step 2.2

Rewrite in slope-intercept form.

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Step 2.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2.2

Write in $y = m x + b$ form.

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Step 2.2.2.1

Reorder terms.

$y = - (\frac{1}{2} x) - 14$

Step 2.2.2.2

Remove parentheses.

$y = - \frac{1}{2} x - 14$

Step 2.3

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.3.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{1}{2}$

$b = - 14$

Step 2.3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{1}{2}$

y-intercept: $(0, - 14)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, - 14)$

Step 2.4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 2.4.1

Write in $y = m x + b$ form.

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Step 2.4.1.1

Reorder terms.

$y = - (\frac{1}{2} x) - 14$

Step 2.4.1.2

Remove parentheses.

$y = - \frac{1}{2} x - 14$

Step 2.4.2

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 14 \\ 2 & - 15 \end{array}$

Step 2.5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- \frac{1}{2}$

y-intercept: $(0, - 14)$

$\begin{array}{c} x & y \\ 0 & - 14 \\ 2 & - 15 \end{array}$

Slope: $- \frac{1}{2}$

y-intercept: $(0, - 14)$

$\begin{array}{c} x & y \\ 0 & - 14 \\ 2 & - 15 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$2 x + 4 y = 28$

$- 2 y = x + 28$

Step 4